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9-3 Geometric Sequences

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9-3 Geometric Sequences & Series Geometric Sequence The ratio of a term to it s previous term is constant. This means you multiply by the same number to get each term. – PowerPoint PPT presentation

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Title: 9-3 Geometric Sequences


1
9-3 Geometric Sequences Series
2
Geometric Sequence
  • The ratio of a term to its previous term is
    constant.
  • This means you multiply by the same number to get
    each term.
  • This number that you multiply by is called the
    common ratio (r).

3
Example Decide whether each sequence is
geometric.
  • 4,-8,16,-32,
  • -8/4-2
  • 16/-8-2
  • -32/16-2
  • Geometric (common ratio is -2)
  • 3,9,-27,-81,243,
  • 9/33
  • -27/9-3
  • -81/-273
  • 243/-81-3
  • Not geometric

4
Rule for a Geometric Sequence
  • ana1rn-1
  • Example Write a rule for the nth term of the
    sequence 5, 2, 0.8, 0.32, . Then find a8.
  • First, find r.
  • r 2/5 .4
  • an5(.4)n-1

a85(.4)8-1 a85(.4)7 a85(.0016384) a8.008192
5
Example One term of a geometric sequence is
a43. The common ratio is r3. Write a rule for
the nth term. Then graph the sequence.
  • If a43, then when n4, an3.
  • Use ana1rn-1
  • 3a1(3)4-1
  • 3a1(3)3
  • 3a1(27)
  • 1/9a1
  • ana1rn-1
  • an(1/9)(3)n-1
  • To graph, graph the points of the form (n,an).
  • Such as, (1,1/9), (2,1/3), (3,1), (4,3),

6
Example Two terms of a geometric sequence are
a2-4 and a6-1024. Write a rule for the nth
term.
  • Write 2 equations, one for each given term.
  • a2a1r2-1 OR -4a1r
  • a6a1r6-1 OR -1024a1r5
  • Use these 2 equations substitution to solve for
    a1 r.
  • -4/ra1
  • -1024(-4/r)r5
  • -1024-4r4
  • 256r4
  • 4r -4r

If r4, then a1-1. an(-1)(4)n-1
If r-4, then a11. an(1)(-4)n-1 an(-4)n-1
Both Work!
7
Formula for the Sum of a Finite Geometric Series
n of terms a1 1st term r common ratio
8
Example Consider the geometric series 421½ .
  • Find the sum of the first 10 terms.
  • Find n such that Sn31/4.

9
log232n
10
H Dub
9-3 Pg.669 3-42 (3n), 53-55, 73-75, 79-81
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